To offer, propose, or report something voluntarily; to put forward a suggestion or request, or to notify/report to someone in authority.
彼はボランティアで手伝いを申し出た。
He offered to help as a volunteer.
問題を上司に申し出るべきだと思う。
I think you should report the problem to your boss.
弁護士が和解案を申し出た。
The lawyer proposed a settlement offer.